JP2015094746A - Effective delayed neutron fraction measurement method and effective delayed neutron fraction measurement apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accurately measure an effective delayed neutron fraction without need of special equipment.SOLUTION: An effective delayed neutron fraction measurement method includes: a test step S100 of acquiring, by an input device, measuring results of multiplication time at a time of withdrawing entire control rods from a critical state and an axial fission fraction distribution of fuel rods; a reactivity, etc., calculation step S200 of calculating a reactivity ρ and an axial extrapolation distance δ; a correction step S300 of calculating an infinite multiplication factor k, and correcting the infinite multiplication factor kfrom a measured value of the axial fission fraction distribution and a measured value of a critical water level zc; a critical-water-level calculation step S400 of calculating the critical water level zc at a time of withdrawal of the entire control rods; and a final-value calculation step S500 of calculating a final value of an effective delayed neutron fraction β. In the reactivity, etc., calculation step S200, a provisional value of the effective delayed neutron fraction βnecessary for calculation is used.

Description

  Embodiments described herein relate generally to an effective delayed neutron ratio measuring method and an effective delayed neutron ratio measuring apparatus for measuring an effective delayed neutron ratio.

  Commercial reactors for power generation require high economic efficiency, but first of all it is essential to ensure safety. Therefore, in order to install a nuclear reactor in the construction of a commercial reactor, it is necessary to study the operational performance of the reactor, and it is necessary to study in detail the stability when a disturbance is applied during steady operation.

  Reactor stability is also called transient characteristics of the reactor.When the reactor is in a steady operation state, even if physical conditions change due to changes in the performance of peripheral equipment that supports the operation state, Detailed examination is made as to whether the operation state can be stably maintained or whether the operation can be stopped safely. For example, in a commercial light water reactor power plant, light water in the core tank is circulated by a motor-driven pump, but even if the rotation speed of this motor changes and the circulation speed of the water in the core changes, the output of the nuclear reactor It is designed not to go up suddenly and into a dangerous state.

  The theory used when investigating with attention paid to changes in reactor power uses a dynamic characteristic equation, and an important concept in the dynamic characteristic equation is a physical quantity called reactivity. Reactivity is a physical quantity that governs temporal changes in nuclear fission reaction (power). Positive reactivity increases the nuclear fission reaction, and negative reactivity decreases the fission reaction. In the case of positive reactivity, the rate of time increase of the fission reaction increases as the value increases.

  The magnitude of the reactivity is discussed by the ratio to the effective delayed neutron fraction, ie the value divided by the effective delayed neutron fraction. The magnitude of the reactivity when the reactivity is equal to the effective delayed neutron ratio is called 1 dollar (dollar). When the reactivity is 1 $, the nuclear fission reaction increases explosively, leading to what is called a reactivity accident. Thus, commercial light water reactors are designed so that in any case, the reactor will not have a positive reactivity of $ 1.

Here, the delayed neutron ratio is a physical quantity that distinguishes neutrons by paying attention to the time difference of neutrons released by the fission reaction. Fission several hundred μsec tens moment fission is, namely 10 and prompt neutrons emitted at about ^-4 second, late be delayed a few tens of seconds from the time of nuclear fission by collapse from fission products (fission fragments) There are neutrons. For example, when ²³⁵ U undergoes fission, about 99.3% of generated neutrons are prompt neutrons and the remaining about 0.7% are delayed neutrons. This delayed neutron plays a major role. If all neutrons generated by fission are prompt neutrons, the time for generating neutrons after fission is about ^10-4 seconds. On the other hand, if 0.7% is delayed neutrons, the effective time from fission to generation of neutrons is about 0.07 seconds.

In the reactor, not only ²³⁵ U but also ²³⁸ U has undergone fission, and ²³⁵ U and ²³⁸ U have different ratios of delayed neutrons. This is an average value obtained by examining the behavior of the fission state in detail. This value is called the effective delayed neutron ratio. Also, as a convention, this value is often called β _eff (beta effective).

  The effective delayed neutron ratio of the core is the most important value when evaluating the effect of reactivity added to or subtracted from the reactor. It can be said that a reactor with a larger effective delayed neutron ratio has less influence on the disturbance that changes the nuclear fission reaction.

  To summarize the above, when evaluating changes (transient characteristics) of a nuclear fission reaction due to a disturbance in a commercial reactor, a quantitative evaluation is performed using the dynamic equation, and the reactivity equation shows the degree of reactivity. The ratio of effective delayed neutrons with large and small scales is a very important physical quantity.

  In addition, before constructing and operating commercial power reactors, reactor physics tests to determine if the fission reaction behaves as designed, and the ability of control rods to stop the fission reaction, etc. In this case, the effect is evaluated using the effective delayed neutron ratio value.

  Thus, the effective delayed neutron ratio is an extremely important basic physical quantity directly related to operation and safety in a commercial power reactor. In this way, the effective delayed neutron ratio is a very important numerical value for grasping the reactor dynamics and reactivity change, and if it can be actually measured by experiment, the validity of the calculation method of the calculation code, This greatly contributes to confirming the quality of the nuclear data used and improving the quality. Therefore, there is a great need and desire to measure the effective delayed neutron ratio by critical experiments.

  On the other hand, this effective delayed neutron ratio is a physical quantity that is extremely difficult to obtain by measurement. Several measurement methods have been proposed so far, but measuring the effective delayed neutron ratio in a commercial reactor for power generation is extremely low in terms of time, economics, and technology. . Therefore, in a commercial nuclear reactor, detailed calculations by a computer are performed using a high-quality computer program (often called computer code) and a well-established nuclear data library, and the effective delay as an average value for the nuclear reactor is calculated. The ratio of neutrons is calculated.

  In this case, check the accuracy and quality of the calculation method, the computer program (computer code) used for the calculation, and the delayed neutrons for each fissile nuclide recorded in the nuclear data library. There is a need.

  Since it is a physical quantity that is directly related to the safety of commercial reactors for power generation, it is extremely important to understand the calculation accuracy of this effective delayed neutron ratio. In order to confirm the reliability of the design and operation of commercial reactors, there is great potential demand for confirming the accuracy of calculating the effective delayed neutron fraction.

Several projects have been carried out to confirm the accuracy of calculating the effective delayed neutron ratio. There is an international benchmark experiment of effective delayed neutron ratio β _eff measurement conducted by Japan Atomic Energy Research Institute (JAERI) and French Atomic Energy Agency (CEA) from 1996 (Heisei 8) to 1998 (Heisei 10). This was a joint experiment between France and Japan aimed at measuring the effective delayed neutron fraction with a critical experiment device for the purpose of comparing with the calculated values.

  The method for measuring the effective delayed neutron ratio is a method of evaluating physical quantities by mathematically processing the signal based on reactor noise (such as neutron detector signal fluctuation), that is, reactor noise (Reactor). noise) based on the theory. Among these methods, the Bennett method (neutron correlation experiment method) was used in this international benchmark experiment.

  The feature of this measurement is the technique of obtaining the measured value from the covariance value by electrically processing the output signal of the neutron detector based on the reactor noise theory and obtaining the measured value. The theory is widely known. In the Bennett method, the electrical signal processing itself is not so difficult from the current computer technology, but in order to correlate the signals of the neutron detectors, at least two kinds of detection characteristics are very similar. A neutron detector is required. On the other hand, the hardware relationship of neutron detectors is not always easy to prepare. For this reason, preparation of the system of the whole experiment is not easy, and time and economical cost are required. In other words, it is not a technique that can be easily applied to any critical experiment apparatus using current equipment.

JP 2008-217139 A

As described above, in the conventional technology, it is necessary to calculate the effective delayed neutron ratio β _eff with high accuracy in terms of design and operation of a commercial nuclear reactor for power generation and safety, There is a requirement (need) to confirm the quality of the calculation code and nuclear data used for the calculation. On the other hand, when the quality of the calculation code and nuclear data is compared with the effective delayed neutron ratio β _eff measured with a critical experiment device, the measurement is not easy, and the problem and solution that a lot of time and economic costs are required There were issues to be addressed.

  Then, embodiment of this invention aims at measuring an effective delayed neutron ratio accurately, without requiring a special apparatus.

In order to achieve the above-described object, the present embodiment maintains a predetermined water level in a core tank that stores a core in which a plurality of fuel rods are arranged at intervals in the horizontal direction, to the core of the control rod. In the effective delayed neutron ratio measurement method for calculating the effective delayed neutron ratio of the critical device that adjusts the insertion length of the critical device to achieve the criticality, the multiplication time t when the control rod is fully extracted from the critical state and the fuel rod A test step in which the input device acquires measurement results of the axial fission rate distribution of the sample, and after the test step, using the multiplication time t and the measurement result of the axial fission rate distribution, the reactivity ρ and the off-axis direction After the step of calculating the reactivity, etc. for calculating the insertion distance δ, and the step of calculating the reactivity, etc., an infinite multiplication factor k _∞ is calculated, and the critical water level zc when the axial fission rate distribution and the core become critical Measurement A correction step of correcting the infinite multiplication factor k _∞ from the value, after said correction step, and the critical water level calculation step of calculating the critical water level zc at full withdrawal of the control rod, after the critical water level calculation step, A final value calculating step of calculating a final value of the effective delayed neutron ratio β _eff , and in the reactivity etc. calculating step, a provisional value of the effective delayed neutron ratio β _eff is calculated, The provisional value of the effective delayed neutron ratio β _eff is used.

Further, in the present embodiment, a control in which a plurality of fuel rods extending in the vertical direction are held in a predetermined water level in a tank that houses a core arranged in a lattice form with a space in the horizontal direction and extended in the vertical direction. An effective delayed neutron ratio measuring device that calculates the effective delayed neutron ratio of a critical device that achieves criticality by adjusting the insertion length of the rod into the core, and an input device that accepts external input of data obtained in experiments An experimental system measurement value storage unit for storing data received by the input device; an experimental system effective delayed neutron ratio provisional value calculation unit for calculating a provisional value of the effective delayed neutron ratio _βeff ; and the experimental system effective delay An experimental system effective delayed neutron ratio provisional value storage unit that stores the provisional value of the effective delayed neutron ratio _βeff calculated by the neutron ratio provisional value calculation unit, and calculates the axial and lateral neutron flows, The calculation of the ratio a of the direction leakage to the axial leakage, the calculation of the multiplication time t based on the signal of the neutron detector stored in the experimental system measurement value storage unit, the multiplication time t and the experimental system effective delay Calculation of the reactivity ρ applied to the critical experiment device using the provisional value of the effective delayed neutron ratio _βeff stored in the provisional neutron ratio provisional value storage unit, the experimental conditions stored in the experimental system measurement value storage unit An experimental system physical quantity calculation unit for calculating a water level zc that becomes critical when all control rods are extracted from the data, and calculating a neutron effective multiplication factor k _eff in a full extraction state of the control rods at the water level during the test, ratio experiment system physical quantity said transverse axial leakage leakage calculated in the operation unit a, the reactivity [rho, the water level zc, stores the calculated result of the such neutron effective multiplication factor k _eff An experimental system axis for calculating an axial output distribution f (x) including an extrapolation distance δ in the axial direction based on the axial output distribution data stored in the experimental system physical quantity storage unit and the experimental system measurement value storage unit A direction extrapolation distance calculation unit, an experiment system axis direction extrapolation distance storage unit that stores an output distribution including an axial direction extrapolation distance calculated by the experiment system axis direction extrapolation distance calculation unit, and the experiment system measurement value storage The infinite multiplication factor k _∞ of the fuel rod cell representing the core system is calculated using the experimental condition data stored in the unit, and the core is calculated using the selected calculation method and calculation code output from the input device. A representative fuel rod cell infinite multiplication factor calculating unit for calculating the effective neutron multiplication factor k _eff ^C of the system, and an infinite multiplication factor k of the fuel rod cell representing the core system calculated by the representative fuel rod cell infinite multiplication factor calculating unit. Representative fuel to remember _∞ The calculation result k _eff ^C of the neutron effective multiplication factor evaluated by the rod cell calculation value storage unit and the experimental system physical quantity calculation unit is compared with the experimental result k _eff ^E, and the absolute value of the difference | k _eff ^C −k _eff ^E | / K _eff ^E is calculated, and the absolute value | k _eff ^C −k _eff ^E | / k _eff ^E is determined to determine whether or not the calculated value / measured value relative error calculating unit; Calculated value / measured value relative error storage unit for storing absolute value | k _eff ^C −k _eff ^E | / k _eff ^E calculated by the calculated value / measured value relative error calculation unit, an appropriate calculation method, and nuclear data library, the calculation code, with the experimental system sensitivity coefficient vector calculating portion for calculating a sensitivity coefficient vector S _E of the effective multiplication factor k _eff of the experimental system, effective in the calculated experimental scheme in the experimental system sensitivity coefficient vector calculation part Multiplication the experimental system sensitivity coefficient vector storage unit for storing the k _eff sensitivity coefficient vector S _E, representative fuel rod cell sensitivity coefficient vector calculation for calculating a sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representing the core and parts, and the representative fuel rod cell sensitivity coefficient vector representative fuel rod cell sensitivity coefficient vector storage unit for storing the sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representative of core calculated by the calculation unit, A covariance error matrix calculation unit for calculating the covariance error matrix W of the nuclear data library, a covariance error matrix storage unit for storing the covariance error matrix W calculated by the covariance error matrix calculation unit, and the experimental system calculation of the relative error E _P of the physical quantity calculation unit is included in the calculated values k _eff ^C was evaluated, and the stored in the experimental system sensitivity coefficient vector storage unit the sensitivity coefficient vector S _E Serial representative fuel rod cell sensitivity coefficient the sensitivity coefficients stored in the vector storage unit vector S _R and the covariance error matrix storage unit the covariance error matrix W stored in the calculation of the correction factor CF with the representative fuel rod cell for relative calculation of the relative error ER _P due to the input parameters using the error E _P and modifiers CF, correction of neutron infinite multiplication factor k _∞ with relative error ER _P due to the input parameters An infinite multiplication factor correction value calculation unit, a ratio of the horizontal leakage to the axial leakage stored in the experimental system physical quantity storage unit, the reactivity ρ, the water level zc, the effective neutron multiplication factor k _eff, etc. When the using the experimental system effective delayed neutron fraction provisional provisional value of the effective delayed neutron fraction beta _eff stored in the storage unit, transfer area M ₁ ² calculation, the second transfer area M ₂ ² Calculating, said transfer area M ₁ ² and the transfer area M ₂ ² and the calculates the synthesized transfer area M ² represent fuel rod cell transfer area calculation unit, calculated by the representative fuel rod cell transfer area calculation unit The final value of the effective delayed neutron ratio β _eff is calculated using the moving area M ² , the corrected k _∞ calculated by the infinite multiplication factor correction value calculation unit of the representative fuel rod cell, the effective neutron multiplication factor k _eff, etc. An experimental system effective delayed neutron ratio calculating unit.

  According to the embodiment of the present invention, the effective delayed neutron ratio can be accurately measured without requiring a special instrument.

It is an elevation sectional view showing the composition of the criticality experiment apparatus which is the target of the effective delayed neutron ratio measuring apparatus according to the embodiment. It is a top view which shows the core of the critical experiment apparatus made into the object of the effective delayed neutron ratio measuring apparatus which concerns on embodiment. It is a top view which shows the other example of the core of the critical experiment apparatus made into the object of the effective delayed neutron ratio measuring apparatus which concerns on embodiment. It is a block diagram which shows the structure of the effective delayed neutron ratio measuring apparatus which concerns on embodiment. It is a block diagram which shows the structure of the calculating part of the effective delayed neutron ratio measuring apparatus which concerns on embodiment. It is a block diagram which shows the structure of the memory | storage part of the effective delayed neutron ratio measuring apparatus which concerns on embodiment. It is a flowchart which shows the whole procedure of the effective delayed neutron ratio measuring method which concerns on embodiment. It is a flowchart which shows the detailed procedure of a test step among the effective delayed neutron ratio measuring methods which concern on embodiment. It is a flowchart which shows the detailed procedure of the calculation steps of reactivity etc. in the effective delayed neutron ratio measuring method which concerns on embodiment. It is a flowchart which shows the detailed procedure of calculation steps, such as correction | amendment, in the effective delayed neutron ratio measuring method which concerns on embodiment. It is a flowchart which shows the detailed procedure and the final value calculation step of a critical water level etc. calculation step among the effective delayed neutron ratio measuring methods which concern on embodiment.

  Hereinafter, an effective delayed neutron ratio measuring method and an effective delayed neutron ratio measuring apparatus according to an embodiment of the present invention will be described with reference to the drawings. Here, the same or similar parts are denoted by common reference numerals, and redundant description is omitted.

  FIG. 1 is an elevational sectional view showing a configuration of a critical experiment apparatus as a target of an effective delayed neutron ratio measuring apparatus according to an embodiment. The present embodiment shows a case where the effective delayed neutron ratio measuring method and the effective delayed neutron ratio measuring apparatus 10 (FIG. 4) are applied to the critical experiment apparatus 200.

The critical experiment apparatus 200 is an apparatus for the purpose of research and development of a commercial furnace for power generation, particularly a light water reactor. The critical experiment apparatus 200 described in this embodiment includes a fuel rod 210 disposed in a core tank 201, a control rod 220 for controlling the reactivity of the core, and a neutron detector 230 for detecting neutrons generated as a result of the reaction. The core tank 201 is a container having an open top, and can store the core 205 and light water (H ₂ O) as a moderator. A water level transmitter 240 for measuring the liquid level in the core tank 201 is provided. The fuel rod 210 has its own weight supported by the fuel support plate 202 at the lower end. The fuel rod 210 is supported at the upper part by the upper lattice plate 203 and at the lower part by the lower lattice plate 204. The outputs of the neutron detector 230 and the water level transmitter 240 are input to the input device 150.

  The criticality experiment apparatus 200 fills the core tank 201 with light water, sets the light water level in the core tank 201 to a certain level determined by the operation procedure, and then controls the core 205 to control the minute reactivity of the core 205. This is a control rod adjustment type that makes the core 205 critical by slightly pulling out the control rod 220 inserted into the core 205. Here, in the case of a core having a fine adjustment rod or a coarse adjustment rod, the control rod 220 usually indicates a control rod for controlling the reactivity.

  FIG. 2 is a plan view showing the core 205 of the critical experiment apparatus which is a target of the effective delayed neutron ratio measuring apparatus according to the embodiment. The nuclear material used in the core of the critical experiment apparatus 200 has a shape similar to that of a fuel in a normal commercial light water reactor fuel assembly, that is, a shape called a fuel rod. The fuel rods 210 are 19 × 19 cores 205 arranged in a 19 × 19 square lattice at regular intervals. Here, the enrichment of the fuel rod 210 is one kind.

  The core 205 has a rectangular parallelepiped shape, a horizontal cross section having a square shape, and extends in the vertical direction. In this case, the reactor core is shaped so that the horizontal and vertical lengths are not too small with sufficient vertical and horizontal lengths. For example, the length of one side of the square in the horizontal section is set to 40 cm or more. Further, the effective critical water level obtained from the effective length of the fuel rod 210 is set to exceed 90 cm. Here, the critical water level is the water level in the core tank 201 when the core 205 achieves criticality.

  Further, the number of fuel rods 210 arranged on one side is desirably an odd number. The purpose of the odd number is to allow the fuel rod 210 located at the center of the core 205 in the horizontal section to exist.

  It is easy to load the core tank 201, that is, to form the core 205 and to remove it from the core tank 201. By measuring the gamma rays emitted from the fuel rods 210, the ratio of the fission reaction can be measured from the emission ratios of the gamma rays at the respective spatial positions of the fuel rods 210.

  FIG. 3 is a plan view showing another example of the core of the critical experiment apparatus which is the target of the effective delayed neutron ratio measurement apparatus according to the embodiment. In this case, the fuel rods 210 are arranged in a 28 × 28 square lattice, which is a 28 × 28 core.

The core system configured as shown in FIGS. 2 and 3 preferably has a rectangular parallelepiped shape. As will be described later, in the embodiment, it is necessary to accurately obtain the ratio of the leakage ratio between the axial direction and the lateral direction of the core system, and it is preferable that the core system has a rectangular parallelepiped shape. The core system is not limited to a rectangular parallelepiped shape. For example, even in the case of a cylindrical system, the present embodiment can be applied if the ratio of the leakage ratio in the axial direction and the lateral direction can be accurately obtained by appropriate measurement and calculation. The fuel rod 210 to be used is generally a UO ₂ fuel rod, but may be a fuel rod containing Pu (plutonium).

FIG. 4 is a block diagram illustrating a configuration of the effective delayed neutron ratio measuring apparatus according to the embodiment.
The effective delayed neutron ratio measuring apparatus 10 can be constructed on a computer. The effective delayed neutron ratio measuring apparatus 10 includes a central processing unit (CPU) 100, a storage unit 130, an input device 150, and an output device 160. The CPU 100 includes a calculation unit 110 and a control unit 140, and the control unit 140 includes an input control unit 141 and an output control unit 142 as a part thereof. Each of these components is connected via the bus 101.

  An input device 150 such as a keyboard or a mouse is connected to the input control unit 141. An output device 160 that performs output and display, such as a printer or a liquid crystal display, is connected to the output control unit 142. Input to the CPU 100 such as an instruction to start calculation to the effective delayed neutron ratio measuring apparatus 10 is performed via the input apparatus 150. Necessary information such as input values necessary for midway calculation, estimated error (uncertainty), and results calculated by the effective delayed neutron ratio measuring apparatus 10 are displayed on the output device 160.

  FIG. 5 is a block diagram illustrating a configuration of a calculation unit of the effective delayed neutron ratio measuring apparatus according to the embodiment. The calculation unit 110 of the CPU 100 includes an experimental system effective delayed neutron ratio provisional value calculation unit 111, an experimental system physical quantity calculation unit 112, an experimental system axial extrapolation distance calculation unit 113, a representative fuel rod cell infinite multiplication factor calculation unit 114, a calculation Value / measurement value relative error calculation unit 115, experimental system sensitivity coefficient vector calculation unit 116, representative fuel rod cell sensitivity coefficient vector calculation unit 117, covariance error matrix calculation unit 118, representative fuel rod cell infinite multiplication factor correction value calculation unit 119 , A representative fuel rod cell moving area calculating unit 120 and an experimental system effective delayed neutron ratio calculating unit 121.

The experimental system effective delayed neutron ratio provisional value calculator 111 calculates a provisional value of the effective delayed neutron ratio β _eff .

The experimental system physical quantity calculation unit 112 calculates the neutron flow in the axial direction and the lateral direction, and calculates the ratio a of the lateral leakage to the axial leakage. Further, the multiplication time t is calculated based on the experimental result. Further, the experimental system physical quantity calculation unit 112 uses the provisional value of the effective delay neutron ratio β _eff calculated by the multiplication time t and the experimental system effective delayed neutron ratio provisional value calculation unit 111 to participate in the critical experiment apparatus 200. The reactivity ρ is calculated. Further, the experimental system physical quantity calculation unit 112 calculates the water level zc that is just critical when all the control rods 220 are extracted based on the experimental condition data, and the control rods 220 are fully extracted at the water level during the test. The neutron effective multiplication factor k _eff is calculated.

  The experimental system axial extrapolation distance calculator 113 calculates the axial output distribution f (x) including the extrapolation distance δ in the axial direction based on the axial output distribution data obtained in the experiment.

The representative fuel rod cell infinite multiplication factor calculation unit 114 calculates the infinite multiplication factor k _∞ of the fuel rod 210 cell representing the system of the core 205 using the experimental condition data, and the selection output from the input device 150. Using the calculated calculation method and calculation code, the neutron effective multiplication factor k _eff ^C of the system of the core 205 is calculated.

The calculated value / measured value relative error calculation unit 116 compares the calculation result k _eff ^C of the neutron effective multiplication factor evaluated by the experimental system physical quantity calculation unit 112 with the experimental result k _eff ^E , and compares the relative error based on the absolute value of the difference. | K _eff ^C −k _eff ^E | / k _eff ^E is calculated, and further, it is determined whether or not the relative error | k _eff ^C −k _eff ^E | / k _eff ^E is equal to or less than a specified value.

The experimental system sensitivity coefficient vector calculation unit 116 calculates the sensitivity coefficient vector S _E of the effective multiplication factor k _eff in the experimental system using an appropriate calculation method, nuclear data library, and calculation code. Representative fuel rod cell sensitivity coefficient vector calculating unit 117 calculates the sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representing the core. The covariance error matrix calculation unit 118 calculates a covariance error matrix W of the nuclear data library.

Representative fuel rod cell infinite multiplication factor correction value calculating unit 119 calculates the relative error E _P experimental system physical quantity calculation unit 112 is included in the calculated values k _eff ^C were evaluated, calculated in the experimental system sensitivity coefficient vector calculation part 116 with a sensitivity coefficient vector S _E representative fuel rod cell sensitivity coefficient sensitivity calculated by the vector calculating unit 117 coefficient vector S _R, and a covariance error matrix W calculated in the covariance error matrix calculation unit 118, modifiers CF is calculated. The representative fuel rod cell infinite multiplication factor correction value calculating unit 119 uses the relative error E _P and modifiers CF, to calculate the relative error ER _P due to the input parameters, the relative error ER caused by the input parameter _{Using P} , the neutron infinite multiplication factor _k∞ is corrected.

The representative fuel rod cell moving area calculation unit 120 includes a ratio of lateral leakage to axial leakage calculated by the experimental system physical quantity calculation unit 112, reactivity ρ, water level zc, neutron effective multiplication factor k _{eff, and the} like. using the provisional value of the effective delayed neutron fraction beta _eff calculated in experimental systems effective delayed neutron fraction provisional value calculating unit 111 calculates the transfer area M ₁ ² and the second moving area M ₂ ^2, this movement to calculate the movement area ^{M 2} obtained by combining the area _M ^{1 2} and transfer area _M ^{2 2.}

The experimental system effective delayed neutron ratio calculating unit 121 includes a moving area M ² calculated by the representative fuel rod cell moving area calculating unit 120 and a corrected neutron calculated by the representative fuel rod cell infinite multiplication factor correction value calculating unit 119. The final value of the effective delayed neutron ratio β _eff is calculated using the infinite multiplication factor k _∞ and the neutron effective multiplication factor k _eff .

  FIG. 6 is a block diagram illustrating the configuration of the storage unit of the effective delayed neutron ratio measuring apparatus according to the embodiment. The storage unit 130 includes an experimental system measurement value storage unit 131, an experimental system effective delayed neutron ratio provisional value storage unit 132, an experimental system physical quantity storage unit 133, an experimental system axial extrapolation distance storage unit 134, and a representative fuel rod cell calculation value. A storage unit 135, a calculated value / measured value relative error storage unit 136, an experimental system sensitivity coefficient vector storage unit 137, a representative fuel rod cell sensitivity coefficient vector storage unit 138, and a covariance error matrix storage unit 139 are provided.

The experimental system measurement value storage unit 131 stores experimental data received by the input device 150. The experimental system effective delayed neutron ratio provisional value storage unit 132 stores a provisional value of the effective delayed neutron ratio β _eff calculated by the experimental system effective delayed neutron ratio provisional value calculation unit 111.

The experimental system physical quantity storage unit 133 stores calculation results such as the ratio of lateral leakage to the axial leakage calculated by the experimental system physical quantity calculation unit 112, reactivity ρ, water level zc, and effective neutron multiplication factor k _eff. To do.

The experimental system axial extrapolation distance storage unit 134 stores an output distribution including the axial extrapolation distance calculated by the experimental system axial extrapolation distance calculation unit 113. The representative fuel rod cell calculation value storage unit 135 stores the infinite multiplication factor k _∞ of the fuel rod cell representing the core system calculated by the representative fuel rod cell infinite multiplication factor calculation unit 114. The calculated value / measured value relative error storage unit 136 stores the absolute value | k _eff ^C −k _eff ^E | / k _eff ^E calculated by the calculated value / measured value relative error calculation unit 115.

The experimental system sensitivity coefficient vector storage unit 137 stores the sensitivity coefficient vector S _E of the effective multiplication factor k _eff in the experimental system calculated by the experimental system sensitivity coefficient vector calculation unit 116. Representative fuel rod cell sensitivity coefficient vector storage unit 138 stores the sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representative of core calculated by the representative fuel rod cell sensitivity coefficient vector calculation part 117. The covariance error matrix storage unit 139 stores the covariance error matrix W calculated by the covariance error matrix calculation unit 118.

  FIG. 7 is a flowchart showing a procedure of an effective delayed neutron ratio measuring method according to the embodiment. First, a control rod pull-out test from the critical state is performed (step S100). The multiplication time is measured in the control rod pull-out test, and the axial power distribution, that is, the fission rate distribution during the test of the fuel rod 210 is measured after the test.

Next, the reactivity ρ and the axial extrapolation distance δ are calculated (step S200). Next, the infinite multiplication factor _k∞ is calculated and corrected (step S300). Next, the critical water level zc when the control rod is completely pulled out is calculated (step S400). Next, the final value of the effective delayed neutron ratio β _eff is calculated (step S500).

  FIG. 8 is a flowchart showing a detailed procedure of a test step in the effective delayed neutron ratio measuring method according to the embodiment. Hereinafter, the procedure of the test step shown in step S100 will be described.

  First, in the critical experiment apparatus 200, the fuel rod 210 and the control rod 220 are installed in the core tank 201, and the neutron detector 230 is attached to configure the target core 205 (step S101).

Next, the core tank 201 is filled with light water to a predetermined height (step S102). At this time, the control rod 220 is inserted into the core 205. When light water is injected into the core tank 201, the effective neutron multiplication factor k _eff increases corresponding to the light water level. The predetermined height of the light water that fills the core tank 201 is a state that does not reach the criticality, that is, a height that maintains the subcritical state, and is a water level lower than the height that reaches the criticality.

After step S102, the insertion length of the control rod 220 into the core 205 is adjusted to bring the core 205 into a critical state (step S103). When the control rod 220 is pulled out from the core 205, the neutron multiplication factor k _{eff of} less than 1.0 increases. Further, by pulling out the control rod 220, the neutron multiplication factor k _eff becomes 1.0, that is, a critical state, and the number of neutrons in the core 205 is kept constant. Let z be the water level of the core tank 201 from which this critical state was obtained. This water level is a predetermined water level determined in advance. Here, what is described as a critical water level is a value called an effective critical water level, which means a measured water level in which the critical water level is converted with the lower end position of the fuel pellet of the fuel rod as the origin (zero). When the core 205 reaches the criticality, a part of the control rod 220 is inserted into the core 205.

  After reaching the critical state in step S103, the light water level z in the core tank 201 in the critical state is output from the water level transmitter 240 and input to the input device 150 (step S104).

After step S104, the control rod 220 is further fully pulled out, that is, the control rod 220 is completely extracted from the core 205 (step S105). By further pulling out the control rod 220 from the critical state, the fission reaction increases, the neutron multiplication factor k _eff exceeds 1.0, the number of neutrons in the core 205 increases, and the signal from the neutron detector 230 increases. . A signal from the neutron detector 230 is input to the input device 150 and stored and stored in the experimental system measurement value storage unit 131. The same applies to measured values such as water level signals.

  If the extraction width is sufficiently large, the increase in the fission reaction per unit period becomes very large, which is dangerous. Therefore, the drawing width is made sufficiently small. That is, based on sufficient preliminary calculation or experimental experience and confirmation so that the length of the control rod 220 inserted into the core 205 is sufficiently short when the core reaches the criticality, Adjust so that the multiplication time at the time of drawing is about 60 to 100 seconds.

  In the state of step S <b> 105, the experimental system physical quantity calculation unit 112 calculates the multiplication time t from the signal of the neutron detector 230 stored in the experimental system measurement value storage unit 131. The multiplication time t calculated by the experimental system physical quantity computing unit 112 is stored and stored in the experimental system physical quantity storage unit 133 (step S106). In the state exceeding the critical condition, the number of neutrons in the core 205 increases exponentially. Therefore, the time when the output of the neutron detector 230 is doubled, that is, the doubling time is constant.

  In the measurement of the multiplication time, if the multiplication time is 60 seconds, the average of measured values cannot be obtained by only one measurement, and there is a problem in measurement accuracy. Therefore, the measurement time of the multiplication time itself is about 3 to 4 times the multiplication time.

  Note that some of the critical experiment apparatuses 200 have a reactivity meter that can display the degree of reactivity added to the experimental system as a numerical value every time. In this case, instead of obtaining the reactivity from the multiplication time by the inverse time equation described later, the reactivity can be measured directly. In this case, the output from the reactivity meter is input to the input device 150.

  In the reactivity meter, a technique called an inverse dynamic characteristic method (IK method: Inverse kinetics) is mainly used. The equation which is the basis of this method is a one-point reactor dynamic characteristic equation, which is a method for evaluating the reactivity with the output signal of the neutron detector as an input. In the reverse dynamic characteristics method, the ratio of each group of the effective delayed neutron ratio of the six-group structure is required, but it is sufficient to use a value obtained by a simple method as in the case of the inverse time equation.

  When the measurement of the multiplication time is completed, if the state in which the control rod 220 is pulled out is held for a long time, it is dangerous because only the output of the core 205 increases. Therefore, as soon as the measurement of the multiplication time is completed, the control rod 220 is inserted again into the core 205 to bring the core 205 below the criticality, or the light water in the core tank 201 is drained to complete the fission reaction. To stop.

  Further, in this step S100, the control extracted from the water level z and the core 205 in the state in which the criticality has been achieved, such as the geometric information of the constructed core system, the atomic number density, the light water level z in the core tank 201, etc. Of the conditional data necessary for the subsequent analysis, such as the length Δx of the rod 220, those other than those automatically input such as the water level z are input from the outside to the input device 150 (step S107). The measurement values and parameters input to the input device 150 are stored in the experimental system measurement value storage unit 131. Therefore, the order of step S107 is not limited after step S106, and may be after any step as long as it is after step S103.

  FIG. 9 is a flowchart showing a detailed procedure of a calculation step of reactivity and the like in the effective delayed neutron ratio measurement method according to the embodiment. Hereinafter, the procedure of the reactivity degree calculation step shown in step S200 will be described.

First, the experimental system effective delayed neutron ratio provisional value calculation unit 111 calculates the provisional value of the effective delayed neutron ratio β _eff of the core system by a reliable calculation using an appropriate calculation code, and this result is calculated as the experimental system effective delayed neutron ratio. The neutron ratio provisional value storage unit 132 stores and stores (step S201). ^{When 235} U and ²³⁸ U are fissioned, neutrons generated can be classified into two types. There are two types: prompt neutrons that occur almost simultaneously with fission, and delayed neutrons that are delayed by seconds from the fission. Delayed neutrons are neutrons that are emitted simultaneously when the fission product produced by fission decays by releasing the energy contained in the nucleus. Here, the number of prompt neutrons and the number of delayed neutrons generated from fission products divided into six groups (6-group structure) are experimentally determined for all neutrons generated when ²³⁵ U and ²³⁸ U undergo fission. There is a table in the form of measurements. The numerical table that is best known in the numerical table and has been used so far is the numerical table based on the measurement of Keepin.

  Both the water level difference method via the inverse time equation and the sample drive method using the output of the reactivity meter based on the inverse dynamics method are based on the one-point reactor dynamics equation. Normally, the leading nuclei of delayed neutrons treated in the one-point reactor dynamics equation are often handled in six groups based on the value of the time constant that decays and emits neutrons. The delayed neutron group is treated as six.

  Although the numerical value related to the delayed neutron is required for both the inverse time equation and the reactivity meter, the numerical value related to the delayed neutron (dynamic characteristic parameter) varies depending on the configuration of the core 205 configured in the critical experiment apparatus 200. Relative values of delayed neutrons with a six-group structure matching the core 205 system are obtained by appropriate preliminary calculations. This value is used for the inverse time equation (Inhour equation) described later or the above-mentioned reactivity meter (Reactivity meter).

Here, the decay constant of the effective delayed _(when dealing with ₆ groups) neutron fraction beta _eff Equation (1), wherein the ratio a _i for each group of effective delayed neutron fraction (2), delayed neutron prior nuclei Is λi (i = 1, 2,..., 6).

Since the purpose of the present embodiment is to obtain the effective delayed neutron ratio β _eff as the measurement value of the critical experiment, it is seemingly impossible to obtain the effective delayed neutron ratio β _eff by calculation. However, it is used as a provisional value here, and is used to improve the accuracy of the effective delayed neutron ratio β _eff finally obtained.

It is strange that the effective delayed neutron ratio (β _eff ^C ) to be finally measured is calculated. However, it is desirable to calculate the effective delayed neutron ratio (β _eff ^C ) used here as accurately as possible, but an error of about ± 10% may be included. This is a provisional value for use in subsequent calculations.

In addition, the value of effective delayed neutron ratio (β _eff ^C ) is about 0.008 (1 $), and the reactivity (excess reactivity) obtained through the multiplication time is 20 ¢ (= 0.20 $). Assuming that the error included in the calculated value of the effective delayed neutron ratio (β _eff ^C ) is 10%, the value estimated as the error is 0.008 × 0.20 × 0.10 = 0.00016 (= 16 pcm), which is a sufficiently small value. This is almost the same value as the uncertainty resulting from the uncertainty of the water level in the critical experiment apparatus 200 that makes the core critical by adjusting the water level. After all, it is not a big problem to use the effective delayed neutron ratio (β _eff ^C ) obtained by calculation during the method as a provisional value.

After step S201, the experimental system physical quantity computing unit 112 stores the multiplication time t calculated in step S106 and stored in the experimental system physical quantity storage unit 133, and the experimental system effective delayed neutron ratio provisional value storage unit 132. The reactivity ρ applied to the critical experiment apparatus 200 is calculated using a provisional value or the like of the effective delayed neutron ratio β _eff . The calculated reactivity ρ is stored and stored in the experimental system physical quantity storage unit 133 (step S202). Here, the reactivity ρ added by substituting the measured multiplication time into the inverse time equation is obtained in dollar ($) units (unit system in which the effective delayed neutron ratio is evaluated as 1 $). As described above, it may be obtained from the value of the reactivity meter. In any case, it is important to obtain the reactivity ρ with high accuracy.

The equation used is called the inverse time equation, and this equation is obtained by Laplace transforming the equation based on the one-point reactor dynamics equation. Here, even if the reactivity (¢) is calculated by substituting the values of ²³⁵ U and ²³⁸ U nuclides alone, which are the above-mentioned widely known Kepin values, into the inverse time equation as the effective delayed neutron ratio. The value of (¢) itself is almost unchanged. The same applies to the processing of the values output by the reactivity meter. In addition, the reactivity which can be calculated | required with a reactivity meter is a $ (dollar) unit.

  The reactivity (in units of $) can be calculated by the inverse time equation of the following equation (3). Here, t is the multiplication time of the neutron flux (or output).

  What is important here is that the numerical value for each group used in the inverse time equation (assuming the normally used 6-group inverse time equation) is the decay constant (related to the decay time). The numerical value) is almost independent of the experimental system and is always a constant value. Second, the numerical value related to the delayed neutron ratio is a relative value for each group (ie, the sum of the six numerical values is 1.00). And since this also has the feature that the rate of change with respect to the experimental system is small, it is possible to calculate the degree of reactivity (in units of $) with sufficient accuracy by simple evaluation. That is, the reactivity is sufficient if it has a reactivity of $ (dollar) unit, and the value of the effective delayed neutron ratio of the experimental system itself is not necessary.

  In order to calculate the reactivity, it seems that a value related to the effective delayed neutron ratio to be finally obtained as a measured value must be prepared in advance and used for the inverse time equation. It is sufficient to calculate the numerical data of delayed neutrons (with 6 groups), for example, based on the basic data for each fission nuclide measured and presented by Keepin, and detailed using computer programs (calculation codes) No special calculation is required. Of course, a value calculated using a computer program may be used.

Calculate the reactivity (¢) by substituting the well-known value of ²³⁵ U and ²³⁸ U nuclides alone into the inverse time equation as is in the data of effective delayed neutron ratio (see equation (2)). However, the value of reactivity (¢) itself is almost unchanged. For example, regarding the second relative value, if it can be estimated that in the critical experimental system, the contribution of ²³⁵ U is 95% and the contribution of ²³⁸ U is 5%, the measured value of Keepin is ²³⁵ U, It is sufficient to take product sums with ²³⁸ U values of 0.95 and 0.05, respectively. The same applies to the processing of the values output by the reactivity meter.

After step S202, the experimental system physical quantity calculation unit 112 calculates the effective neutron multiplication factor k _eff when the control rod 220 is fully pulled out. The calculated effective neutron multiplication factor k _eff is stored and stored in the experimental system physical quantity storage unit 133 (step S203). After making the system of the core 205 configured in the critical experiment apparatus 200 critical, when the control rod 220 is pulled out from the core 205 by a very small length, the fission reaction and the output of the core 205 start to increase. If the multiplication time is measured based on the signal from the neutron detector 230 and an inverse time equation is used, or if a reactivity meter (not shown) is used, the reactivity ρ added to the system of the core 205 as described above. ($ Units) can be obtained. Therefore, the reactivity ρ obtained through the inverse time equation by measuring the multiplication time and the reactivity ρ obtained using the reactivity meter are in units of $ (dollar).

The unit of the numerical value of the reactivity (ρ) added to the core from the multiplication time through the inverse time equation with the control rod 220 pulled out is a unit of dollar ($) (the effective delayed neutron ratio is evaluated as 1 $). Therefore, the effective delayed neutron ratio (β _eff ^C ) obtained by calculation is multiplied and the value is added to 1.000 to obtain the effective neutron multiplication factor (k _eff ^E ). The relative difference between this value and the calculated effective neutron multiplication factor (k _eff ^C ) is important, and this relative difference will be used later.

In the critical state where the control rod 220 is inserted into the core 205 and the core 205 becomes critical, the effective neutron multiplication factor (k _eff ^E ) is physically 1.000. If this state is calculated, it seems that it is not necessary to calculate the effective delayed neutron ratio (β _eff ^C ). On the other hand, the state where the control rod 220 is inserted into the core 205 must be calculated. In general, it is very difficult to calculate with the control rod 220 inserted with high accuracy. This is because it is necessary to accurately evaluate the reaction between the control rod 220 and the neutron. Therefore, calculation in a state where the control rod 220 is not inserted into the core 205 is preferable.

  After step S203, the experimental system axial extrapolation distance calculation unit 113 evaluates the axial power distribution of the reactor core system and the extrapolation distance δ in the axial direction. The experimental system axial direction extrapolation distance storage unit 134 stores and stores this result (step S204). For this purpose, the fuel rod 210 at an appropriate position in the center of the core 205 is extracted. When the core 205 is a 19 × 19 type system with an odd number of sides, the fuel rod 210 is located at the center of the core 205, so that fuel rod 210 is used. In the case of a system in which the core 205 is composed of an even number of sides such as a 28 × 28 type, the fuel rod 210 as close to the center of the core 205 as possible is used. An integral γ-ray measurement (not shown) is performed with respect to the axial direction of the extracted fuel rod 210 to obtain an axial power distribution of the core 205. The measurement result is input to the input device 150 and stored and stored in the experimental system measurement value storage unit 131.

  The experimental system axial extrapolation distance calculation unit 113 fits the obtained axial output distribution data to a cosine curve with an appropriate calculation code, and then includes the extrapolation distance δ in the axial direction. The axial output distribution f (x) is calculated by the equation (4). Here, L is an effective length of the fuel rod (length in the axial direction in which the pellet is filled), and δ is a value called an extrapolation distance. The experimental system axial direction extrapolation distance storage unit 134 stores this output distribution.

  When measurement is difficult, the axial fission rate distribution (output distribution) of the target fuel rod 210 may be obtained by calculation using an appropriate calculation code. In this case, in order to increase the calculation accuracy, calculation is performed in a state where the control rod 220 is pulled out from the core 205. Due to the calculation theory and the quality of the calculation values used in the current reactor calculation code, in the criticality experiment of such a rectangular parallelepiped system with high homogeneity, the calculated values after normalizing each with very high accuracy The measured values can coincide.

  Although calculation based on diffusion theory can be used, it is desirable to use a transport calculation code in order to obtain a higher quality calculation value. As a three-dimensional transport calculation code based on determinism, for example, there is a DANTSYS system.

  Further, a continuous energy general-purpose Monte Carlo code may be used. The Monte Carlo code is a method that uses random numbers to solve the integral Boltzmann transport equation. However, it is desirable because it can handle the calculation system geometrically very accurately and has a very high approximation accuracy. Is determined by the time required for the calculation.

  Here, firstly, it is assumed that a multi-group energy three-dimensional transport calculation code based on determinism rather than Monte Carlo calculation is used. Normalize the axial fission rate (output) distribution obtained in the criticality experiment (or calculation), and measure the number of points including the position with the largest value, excluding the measurement value near the top or bottom of the fuel rod. Are fitted in the function form of Equation (4) above by an appropriate computer program (or a commercially available PC application).

  In general, the extrapolation distance δ is a value inherent to the critical experiment apparatus 200, and it has been empirically found that the dependence on the individual core system constructed in the critical experiment apparatus 200 is small. Therefore, if a reliable value of extrapolation distance δ obtained in another experiment is given, that value can be used.

Note buckling Bz ² in the axial direction is expressed by the following equation (5).

  FIG. 10 is a flowchart showing a detailed procedure of a correction calculation step in the effective delayed neutron ratio measurement method according to the embodiment. Hereinafter, the procedure of the correction calculation step shown in step S300 will be described.

First, a calculation method, a nuclear data library, and a calculation code are selected and externally input to the input device 150 (step S301). The selection result is output from the input device 150 to the representative fuel rod cell infinite multiplication factor calculation unit 114. The representative fuel rod cell infinite multiplication factor calculation unit 114 calculates the effective neutron multiplication factor k _eff ^C of the core system using the selected calculation method and calculation code. The calculated effective neutron multiplication factor k _eff ^C is stored and stored in the representative fuel rod cell calculated value storage unit 135 (step S302).

After step S302, the calculated value / measured value relative error calculation unit 115 compares the calculation result k _eff ^C of the neutron effective multiplication factor with the experimental result k _eff ^E , and | k _eff ^C −k _eff ^E | / k _eff ^E Is calculated. The calculated value / measured value relative error calculation unit 115 further determines whether or not the value | k _eff ^C −k _eff ^E | / k _eff ^E is equal to or less than a specified value. The calculated value / measured value relative error storage unit 136 stores and stores the value | k _eff ^C −k _eff ^E | / k _eff ^E and the determination result. (Step S303). Originally, the calculation result k _eff ^C should be physically equal to the experimental result k _eff ^E , but a deviation occurs due to an error based on the calculation method of the nuclear data library and calculation code. If the absolute value of this difference is large and does not fall below the specified value (NO in step S303), the calculation accuracy cannot be guaranteed, and the output device 160 displays that fact. The display by the output device 160 returns to step S301 again, and the calculation method, the nuclear data library, and the calculation code are reviewed again and examined.

  When the absolute value of the difference is equal to or less than the specified value and it can be determined that the calculation accuracy is sufficient (YES in step S303), the experimental system physical quantity calculator 112 uses the calculation method, the nuclear data library, and the calculation code in the axial direction and the horizontal direction. Neutron flow is calculated, and a ratio a of lateral leakage to axial leakage is calculated (step S304).

After step S304, the experimental system sensitivity coefficient vector calculation unit 116 calculates the sensitivity coefficient vector S _E of the effective multiplication factor k _eff in the experimental system using an appropriate calculation method, nuclear data library, and calculation code. The experimental system sensitivity coefficient vector storage unit 137 stores the sensitivity coefficient vector S _E of the effective multiplication factor k _eff in this experimental system (step S305). Note that the calculation method, the nuclear data library, and the calculation code are not necessarily the same as those used in step S304.

After step S305, the representative fuel rod cell infinite multiplication factor correction value calculation unit 119 calculates the infinite multiplication factor k _∞ of the fuel rod cell representative of the core system, and the infinite number of fuel rod cells representative of the calculated core system. multiplication factor k _∞ representative fuel rod cell calculation value storage unit 135 stores (step S306). It is very difficult to obtain the infinite multiplication factor _k∞ by measurement. Here, the calculated value is obtained by correcting the calculated value with the measured value of the critical experiment. The infinite multiplication factor k _∞ applied to the modified group 1 diffusion equation described below may be considered to be the same as the neutron infinite multiplication factor k _{∞ of} the fuel rod cell for the fuel rod 210 configured in the critical experiment apparatus 200. . The infinite multiplication factor of the fuel rods the cell k _∞ it is difficult to determine by the measurement, obtained by calculation.

It is not difficult to calculate the infinite multiplication factor k _∞ of this fuel rod cell using current nuclear power calculation techniques. On the other hand, since the nuclear data library used for the calculation includes errors and uncertainties, even if the calculation method is sufficiently accurate, the nuclear data library that is the input parameter for the calculation calculates the infinite multiplication factor k _∞ of the fuel rod cell. An error may occur in the value.

  Therefore, this time, using the measurement value of this critical experiment, which is sufficiently simulated, the calculation code for calculating the infinite multiplication factor of the fuel rod cell and the nuclear data library will be used to correct the calculated value.

  In the present embodiment, it is assumed that the number of cases of simulation experiments that can be performed or that can be used is one. Here, the subscript R indicates the target fuel rod cell, and the subscript E indicates the simulation experiment system as described above.

  As already mentioned, it is possible to define a sensitivity coefficient for the calculation input parameter that is focused on the design value (= numerical value indicating performance) of the target product or facility, and there are multiple calculation input parameters. Sensitivity coefficients are obtained, and sensitivity coefficient vectors having these as components are defined.

Here, a calculation input parameter (nuclear cross section, etc.) of a physical quantity (reactivity, etc.) of interest, S _R is a sensitivity coefficient vector for a target reactor facility, and S _E is a sensitivity coefficient vector for a simulation experiment. Also, let W be a covariance (error) matrix that represents the uncertainty of calculation input parameters (such as nuclear cross section).

Next, the representative fuel rod cell sensitivity coefficient vector calculation unit 117, endless fuel rod cell and calculating a sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representing the core, representative of the calculated core the sensitivity coefficient vector _{S R} of the multiplication factor k _∞ representative fuel rod cell sensitivity coefficient vector storage unit 138 stores (step S307).

  Next, the covariance error matrix calculation unit 118 calculates the covariance error matrix W of the nuclear data library, and the covariance error matrix storage unit 139 stores and stores the calculated covariance error matrix W (step S308). . In principle, the covariance error matrix is defined for all the inputs used in the simulation, but if the evaluation is very difficult, the covariance error matrix may be a diagonal matrix.

  In the embodiment, a measured value of effective delayed neutrons is obtained by mainly combining conventional methods well known in the nuclear technology field. The measured value of the effective delayed neutron ratio is obtained based on a numerical value obtained by a normal nuclear calculation method to obtain a final value. What is required for the calculation is to calculate a sensitivity coefficient vector related to the nuclear data library for the neutron effective multiplication factor of the critical experiment apparatus 200, and to use the covariance error matrix W of the nuclear data library to represent the representative factor (Representative factor). ) Is used (a SCALE system developed at the National Laboratory in the United States is currently available). In addition, a calculation code capable of transporting the critical experiment apparatus 200 in a three-dimensional system (a DANTSYS system developed in the United States is currently available) is required.

  The SCALE system is a nuclear power calculation code system developed at Oak Ridge National Laboratory, which was developed at the request of the US Nuclear Regulatory Commission for use in criticality safety assessments in the United States. This system combines a code, fuel calculation code, evaluated nuclear data library, etc., and can perform criticality calculation, sensitivity analysis calculation, combustion calculation, and radiation dose evaluation calculation.

  The DANTSYS system is a system for performing criticality calculations to determine whether a reactor system is critical or not, with the space subdivided for a system described in a 2D system or a 3D system. It is a calculation code that performs neutron transport calculations using a deterministic method. In general, if a neutron transport calculation is performed by a deterministic method, a very long calculation time is required. However, in DANTSYS, a mathematical acceleration method for shortening the calculation time is used.

  The theory underlying this embodiment is a one-point reactor dynamics equation representing the time variation of the nuclear fission reaction in seconds, an inverse time equation derived from the dynamic equation, and the critical state of the reactor This is a modified first group diffusion equation that simply expresses the above conditions.

After step S308, the representative fuel rod cell infinite multiplication factor correction value calculation unit 119 has calculated the sensitivity coefficient vector S _E experimental system sensitivity coefficient vector calculation part 116 calculates a representative fuel rod cell sensitivity coefficient vector calculation part 117 a sensitivity coefficient vector S _R, the covariance error matrix using the covariance error matrix W calculated in the operation unit 118, neutron effective multiplication factor k _eff and infinite neutron multiplication factor k _∞ between modifiers CF the following formula It calculates by (6) (step S309).
^{_{CF = (S R T WS R}} ) / (S E T WS R) ... (6)

  Here, the concept regarding the calculation of the correction factor CF will be described below.

A representative factor (or simulation evaluation factor) RF can be defined as an index indicating how similar the simulation experiment is to the design value of the target product or facility on the calculation simulation. The representative factor (or simulation property evaluation factor) RF is expressed by the following equation (7) using sensitivity coefficient vectors S _E and S _R and a covariance (error) matrix W.
^{_{RF = S E T WS R /}} {(S E T WS E) 1/2 (S R T WS R) 1/2} ... (7)

If the magnitude of the sensitivity coefficient vector via the covariance error matrix W is considered as follows,
a = (S _E ^T WS _E ) ^1/2 , b = (S _R ^T WS _R ) ^1/2
If the angle formed by the sensitivity vectors S _E and S _R via the covariance (error) matrix is an angle θ, the representative factor RF corresponds to cos θ as shown in the following equation.
^{_{RF = S E T WS R /}} (ab)
Therefore, the following expression (8) is satisfied.
−1 ≦ RF ≦ 1 (8)

  As described above, one case of a simulation experiment (critical experiment) in which the absolute value of the representative factor (or simulation evaluation factor) RF is sufficiently large (close to 1.0) is selected. The objective system is the core rod fuel rod cell (two-dimensional system in which the used fuel rods are positioned at the center of a square grid with one side of the fuel rod pitch) constructed in the critical experiment apparatus 200, and the simulation experiment is the core system. is there.

Next, a correction factor (CF) is considered as follows. The length obtained by projecting the sensitivity coefficient vector S _E in the direction of S _R, so is kcos, illusory error of a ratio simulate systems of the length of the vector S _R when aligned in the direction of the vector S _R Is considered as a correction factor CF of how the error appears in the product or facility, the correction factor CF is obtained by the following equation (9).

Here, b ² is as follows.
_{^{b 2 = {(S R T}} WS R) 1/2} 2 = S R T WS R
After all, the correction factor CF becomes the following equation (10), which is a natural definition.
_{^{CF = (S R T WS R}} ) / (S E T WS R) ... (10)
Since the numerator of equation (10) is always a positive value, the sign of correction factor CF is determined by the sign of denominator S _E ^T WS _R.

After step S309, the representative fuel rod cell infinite multiplication factor correction value calculating unit 119, a representative fuel rod cell infinite multiplication factor correction value calculating unit 119 for calculating the relative error E _P included in the calculation value k _eff ^C is experimental system The relative error E _P included in the calculated value k _eff ^C evaluated by the physical quantity calculation unit 112 is calculated (step S310).

The nuclear characteristic R of the selected critical experiment is the critical eigenvalue (neutron effective multiplication factor). The neutron effective multiplication factor (k _eff ^C ) with the control rod 220 pulled out is evaluated. The calculated value k _eff ^C of the effective neutron multiplication factor is obtained by the same method (the same nuclear data library and the same calculation code) for calculating the reactivity of the product (fuel assembly etc.) intended for the criticality experiment. As described above, the relative error E _P included in the calculated value k _eff ^C is ((k _eff ^C −k _eff ^E ) / k _{eff, based on} the value k _eff ^E of the effective neutron multiplication factor obtained in the critical experiment. ^E )), that is, (k _eff ^C / k _eff ^E −1).

Based on the relative error (k _eff ^C / k _eff ^E −1) between the measured value and the calculated value of the critical experiment, excluding the relative error caused by the calculation method, the relative error of the measured value of the critical experiment, or The relative error E _P caused by the error of the calculation input parameter is evaluated according to the concept shown. In evaluating the relative error E _P , it is necessary to satisfy the following requirements.

  The calculation model used must have sufficient accuracy when calculating the physical quantity of interest and does not cause calculation errors characterized by the calculation model used. For example, in the nuclear power field, nuclear materials are sometimes loaded into a very small system, but if such a system is calculated with a simple nuclear data library that handles diffusion calculations and energy groups with a small number of groups, the quality of the calculation model is sufficient. Therefore, a calculation error occurs. A sufficiently detailed calculation method should be used to avoid such errors. For example, general-purpose Monte Carlo calculation using a continuous energy library is appropriate. Again, the system and product geometric descriptions should be sufficiently detailed to avoid errors in the description of geometric shapes.

  It should be noted that errors in numerical calculations themselves can be ignored. In addition, it should be noted that the statistical error is sufficiently small when Monte Carlo calculation is applied.

  The measurement error for the experiment must also be sufficiently small.

Note that statistical errors and experimental measurement errors that occur when Monte Carlo calculation is applied to numerical calculations are not systematic errors with systematicity in any case, but are classified as random errors with positive and negative values varying depending on the case. Think. Therefore, these errors are treated as “uncertainty” and are not directly related to the evaluation of the relative error E _P.

After step S310, the representative fuel rod cell infinite multiplication factor correction value calculating unit 119 uses the relative error _{E P} and modifiers _CF, calculated relative error ER _P due to the input parameters as ER P = _{E P} × CF (Step S311). Based on the relative error E _P caused by the error of the calculation input parameter obtained from the measured value and the calculated value for the physical quantity of interest by conducting a simulation experiment, the design calculated value of the target product or facility is relative error ER _P due to errors in the calculation input parameter is expressed by the following equation (11).
_{ER P = E P × CF =} E P × (S R T WS R) / (S E T WS R) ... (11)

It should be noted here that, the value of E _P is given definite positive and negative, and because modified Factor CF is also given by definite values of positive and negative, for design calculation value of a product or property of interest, calculation input relative error ER _P due to the error of the parameters are calculated automatically definite positive and negative. For the above calculation, a SCALE system developed by a national laboratory in the United States can be applied.

After step S311, the representative fuel rod cell infinite multiplication factor correction value calculating unit 119 stores corrects the neutron infinite multiplication factor k _∞ with relative error ER _P due to the input parameters (step S312). That is, using the relative error ER _P obtained in step S311, the infinite multiplication factor k _∞ of the fuel rod cells of interest, using a value corrected by the following equation (12). Thus, an infinite multiplication factor k _∞ reflecting the result of the critical experiment is obtained.
_k∞ (after correction) = _k∞ (first calculation result) × 1 / (1 + ER _P ) (12)

  FIG. 11 is a flowchart showing the detailed procedure of the critical water level calculation step and the final value calculation step in the effective delayed neutron ratio measurement method according to the embodiment. Hereinafter, the detailed procedure of the critical water level calculation step shown in step S400 will be described.

The calculation of the neutron effective multiplication factor k _eff ^C uses a modified first group diffusion equation. The modified group 1 diffusion equation is expressed as follows, where the effective neutron multiplication factor is k _eff , the infinite neutron multiplication factor is k _∞ , the movement area (Migration area) is M ² , and the whole system buckling is B ^2. 13).

この式の特徴は原子炉の中性子束に関してエネルギーによる差を考慮せず、すなわち中性子エネルギーを１つの群として扱う考え方であり、ここに記載されているバックリングも中性子束のエネルギーには依存せず、同じ値であるという仮定がなされている。

The characteristic of this equation is that it does not take into account the difference in energy with respect to the neutron flux of the reactor, that is, the idea of treating the neutron energy as one group, and the buckling described here does not depend on the energy of the neutron flux. , The same value is assumed.

In the present embodiment, numerical processing is performed by assuming that the axial neutron flux follows the cosine distribution with respect to the modified first group diffusion equation. In the normal critical experiment apparatus 200, the axial direction often has the same core cross section at any position with respect to the effective length position of the fuel rod, and can be regarded as homogeneous. Therefore, the axial neutron flux distribution may be considered as a cosine distribution. In this case, the core in the axial direction of Buckling _{(buckling) B} ^{Z 2} is a circular constant [pi, the effective water level z, the extrapolation distance [delta], represented by the preceding formula (5).

  In addition, what is described as an effective water level here is a value referred to as an effective critical water level, which means a measured water level in which the critical water level is converted with the lower end position of the fuel pellet of the fuel rod as the origin (zero).

Furthermore, in this reactivity measurement, the measurement is started from the critical state and the reactivity to be changed is not so large. That is, even if a reactivity change is brought about in the core, the effective neutron multiplication factor (k _eff ) can always be regarded as about 1.00. Using this assumption and based on the modified first group diffusion equation, the water level reactivity coefficient can be expressed as 1/3 of (effective water level + extrapolation distance).

The theoretical formula of the water level reactivity coefficient used in this embodiment will be described including derivation. Consider a case where the following three assumptions (a) to (c) hold.
(A) The modified group 1 diffusion equation can be applied in the experimental system, and in order for this assumption to be sufficiently established, it is necessary that the core system configured in the critical experiment apparatus 200 is not excessively small.
(B) The core axis direction distribution can be approximated by a cosine distribution. In order for this assumption to be fully established, the axial configuration of the core 205 configured in the critical experiment apparatus 200 is homogeneous, that is, the radial configuration of the core 205 is not different at the axial position, In other words, it is important that the radial configuration is the same at any position in the axial direction. Of course, the core system is not strictly homogeneous in the axial direction. There is a structure such as a lower lattice plate for inserting and supporting the fuel rods in the lower part in the core axis direction, and there is an upper lattice plate and air in the upper part. Here, it is sufficient if the configuration is homogeneous in the axial direction within the effective length range of the fuel rod.
(C) The water level difference is about several cm to 10 cm with or without the measurement sample.

Based on the above assumptions, a formula for processing the reactivity is derived. Now, a virtual infinite multiplication factor of the radial cross section of the core system k _∞, the Buckling of the transverse direction of the core system (radial) A (usually _B ^{r 2} and the display), the movement area of the core system ^M 2, The core effective axial height is z, and the axial extrapolation distance is δ. The core axial height z varies, but other values are assumed to be constant during this experiment (period). Assuming that the circumference is π and the axial neutron flux distribution is assumed to be a cosine distribution, the buckling in the core axis direction is expressed as shown in the above equation (5).

As a result, the effective neutron multiplication factor k _eff of the core is expressed by the following equation (14) in the modified first group diffusion theory.

The ^{B 2} in formula (14) is a Buckling of the whole system is the sum of the radial and axial direction.

Next, if the neutron effective multiplication factor k _eff is partially differentiated with respect to the core effective axial direction length z, the following equation (15) is obtained.

On the other hand, the reactivity ρ is expressed by the following equation (16) using k _eff , and if the reactivity ρ is partially differentiated by the core effective axis direction length z, equation (17) can be obtained.
ρ = (k _eff −1) / k _eff = 1−1 / k _eff (16)

  If the equation (15) is substituted into the equation (17), the water level reactivity coefficient regarding the water level, that is, the effective axial direction length z is obtained by the following equation (18).

  Hereinafter, the procedure of each step of the final value calculation step shown in step S500 in FIG. 11 will be described.

First, the representative fuel rod cell moving area calculation unit 120 calculates the moving area M ₁ ² (step S401). Specifically, the ratio of the lateral leakage to the axial leakage stored in the experimental system physical quantity storage unit 133, the reactivity ρ, the effective neutron multiplication factor k _{eff, and the} like, and the experimental system effective delayed neutron ratio provisional value using the provisional value of the effective delayed neutron fraction beta _eff stored in the storage unit 132, by the following equation (19), calculates a first transfer area M ₁ ^2.

  In addition, u is the reciprocal of the uncertainty of this calculation or an appropriate weight.

  Further, the experimental system physical quantity calculation unit 112 calculates a water level zc that becomes just critical when all the control rods are pulled out from the following equation (20). The calculated water level zc is stored and stored in the experimental system physical quantity storage unit 133 (step S402).

The effective neutron multiplication factor k _eff of the core is expressed by the following formula (21) in the modified first group diffusion theory.

Here, A is the buckling in the radial direction, but it is very difficult to accurately obtain this value from the measurement.
When obtaining from the measurement, integral γ measurement is performed in the radial direction of the core system, and the power distribution in the radial direction of the core system is obtained. This radial axial fission rate (output) distribution is normalized, and the measured value of a plurality of points including the position having the largest value is expressed by the following equation (22) by an appropriate computer program (or commercially available PC application). Fit in shape.

この場合、Ｌは炉心体系の横方向の有効長（通常は燃料棒ピッチ×燃料棒セル数）、Δは横方向外挿距離と呼ばれる値である。このようにして外挿距離Δを得る。

In this case, L is a laterally effective length of the core system (usually fuel rod pitch × number of fuel rod cells), and Δ is a value called lateral extrapolation distance. In this way, the extrapolation distance Δ is obtained.

In general, it is empirically known that the extrapolation distance Δ is a value inherent to the critical experiment apparatus 200 and has a small dependency on the individual core system constructed in the critical experiment apparatus 200. Therefore, if a reliable value of extrapolation distance Δ obtained in another experiment is given, that value can be used. The lateral buckling B _X ² is represented by the following formula (23).

In this case, there are two horizontal directions, the X direction and the Y direction, which are twice the value of Expression (23), and therefore are expressed as the following Expression (24).
a = 2 × B _X ² / B _Z ² (24)

  Usually, evaluation of a uses the calculated value of the three-dimensional transport calculation code. Even in this case, the continuous energy general-purpose Monte Carlo code can be evaluated. However, in this embodiment, it is preferable to use the three-dimensional transport calculation code among the deterministic codes because of the simplicity of calculation and the good consistency. Recommended first.

In a three-dimensional transport calculation code in which neutron energy is handled in multiple groups (10 groups or more), a rectangular parallelepiped core 205 is calculated with a detailed spatial mesh, and a neutron leakage ratio for each of the six surfaces is obtained as a calculation output. From the calculated values, the sum of the ratios of neutron leakage on the upper and lower surfaces in the axial direction (axial leakage) and the sum of the ratios of leakage on the four lateral surfaces (lateral leakage) are calculated to obtain the ratio. That is, when calculating how many times A is B _Z ² and assuming that ratio is a, the effective neutron multiplication factor k _eff is given by the following equation (25).

Since the core system of the critical experiment apparatus 200 exceeds the critical water level z and the criticality in the state where the control rod 220 is pulled out, and the effective neutron multiplication factor k _eff is k _eff = k _eff ^E , the equation (25) from transfer area ^{M 2} is determined by the following equation (26). Now, representing the ^{M 2} and _M ^{1 2.}

  In the case where the water level of the core tank is z and the control rod or fine adjustment rod is pulled out of the core, this critical experiment apparatus 200 is a core tank that has achieved criticality by an experimental apparatus that achieves criticality by adjusting the water level of the core tank water. It is assumed that the water level zc is exceeded. Since the water level of the core tank water that achieves the criticality is zc, the following equation (27) is obtained if the critical condition is described by a modified first group equation.

  The experimental system physical quantity calculator 112 solves the equation (27) to obtain the critical water level zc as in the following equation (28).

Next, the representative fuel rod cell transfer area calculation unit 120 further calculates the second transfer area _M ^{2 2} (step S403). Specifically, the ratio a of the lateral leakage to the axial leakage stored in the experimental system physical quantity storage unit 133, the reactivity ρ, the effective neutron multiplication factor k _eff , zc, etc., and the effective delayed neutron ratio of the experimental system by using the provisional value of the effective delayed neutron fraction beta _eff stored in provisional value storage unit 132, calculates a second transfer area M ₂ ² by the following equation (29).

  Furthermore, v is the reciprocal of the calculation uncertainty or an appropriate weight.

  Now, assume that the water level of the core tank 201 in the state where the control rod 220 is pulled out from the core 205 is z, and the water level has risen from the critical water level zc and the reactivity is added.

  As described above, the multiplication time is obtained based on the increase in the indicated value of the reactivity neutron detector obtained from the multiplication time t measured when the control rod 220 is pulled out, and the inverse time equation is obtained. The reactivity ρ applied to the critical experiment apparatus 200 is obtained by a reactivity meter based on the inverse dynamics method (Inverse kinetics), the unit being dollar ($) unit (effective delayed neutron ratio is 1) Unit system evaluated as $).

The effective delayed neutron fraction of the core system configured in the critical experiment apparatus 200 is calculated using a computer program (calculation code) generally accepted in the nuclear field and a nuclear data library. For example, the calculation code is the DANTSYS system, and the nuclear data library is JENDL-4.0. Usually, this calculation value may have an error of ± several% to 10% due to uncertainty or error in the numerical value of the calculation method and the yield of delayed neutrons stored in the nuclear data library. It is said. If this numerical value is the effective delayed neutron ratio β _eff , the water level reactivity can be replaced with a dimensionless numerical value by multiplying the value of the reactivity (in units of $). However, it should be noted that this value may cause an error of about ± several% to 10%.

If the difference between the critical water level zc and the water level z of the already obtained core tank water is Δz (Δz = z−zc),
zc + Δz / 2 = zc + (z−zc) / 2 = (z + zc) / 2
Therefore, the following equation (30) is modified to obtain the following equation (31). Using equation (31), movement area ^{M 2} is obtained by equation (32). M ² obtained by this formula (32) is represented as M ₂ ² .

Next, the representative fuel rod cell transfer area calculation unit 120 calculates the movement area ^{M 2} synthesized by the following equation (33) (step S404).

In general, M ₁ ² obtained by Expression (26) does not match M ₂ ² obtained by Expression (29). This is because a in formula (26) includes calculation uncertainty, and the effective delayed neutron ratio β _eff in formula (29) also includes calculation uncertainty. Originally, an attempt is made to obtain the effective delayed neutron ratio β _eff of the core configured in the critical experiment apparatus 200 using the measured value of the critical experiment, and therefore, using the calculated effective delayed neutron ratio β _eff ( It tends to be thought that M ₂ ^{2 obtained} in 29) has no meaning, but it is not so. A procedure for obtaining a more effective effective delayed neutron ratio β _eff starting from an effective delayed neutron ratio β _eff having a certain degree of correctness is valid.

Therefore, an attempt is made to obtain a more appropriate moving area M ² using M ₁ ² obtained by Expression (26) and M ₂ ² obtained by Expression (32). Here, the least square method is used. That is, using the appropriate weights u and v, x that minimizes the function f (x) in the following equation (34) is the moving area M ² that is determined to be the most appropriate.
f (x) = u (M ₁ ² −x) ² + v (M ₂ ² −x) ² (34)
From the extreme value condition that minimizes f (x), the following equation (35) is obtained.

On the other hand, the following equation (36), can be obtained transfer area M ² to definitively found.
x = M ² = (uM ₁ ² + vM ₂ ² ) / (u + v) (36)
For u and v, the reciprocal of the estimated calculation error of M ₁ ² obtained by Expression (26) and M ₂ ² obtained by Expression (29) may be used. Note that when it is determined that it is not preferable to use the calculated effective delayed neutron ratio β _eff when finally obtaining the effective delayed neutron ratio β _eff , v is much higher than u. A small number or 0 can be used.

After step S400 is completed, the experimental system effective delayed neutron ratio calculating unit 121 calculates the final value of the effective delayed neutron ratio β _eff (step S500).

First, the measurement method of the effective delayed neutron ratio, that is, the basic measurement principle will be described. The effective delayed neutron ratio β _eff can be determined from the measured value of the water level reactivity coefficient. Reactor core and has achieved critical in the core tank water level z _0. The reactor tank water level is increased by Δz ₀ and the reactivity applied to the core is measured. When the water level reactivity coefficient at the height of the core tank water level z ₀ + 0.5Δz ₀ at this time is calculated from the equation (31) in units of $ (that is, a value divided by the effective delayed neutron ratio β _eff ), Expressions (37) and (38) are obtained.

Therefore

In equation (38), π is a constant, z ₀ and Δz ₀ are usually measured values, and ρ is obtained as a measured value in $ units through measurement of multiplication time. Therefore, if the moving area M ² , the infinite multiplication factor k _∞ , and the extrapolation distance δ can be obtained, the effective delayed neutron ratio β _eff can be obtained. This is the basic measurement principle in the present embodiment.

  All the necessary numerical values have been obtained by the previous steps. By substituting the respective numerical values into the equation (38), the effective delayed neutron ratio can be obtained as in the following equation (39).

In particular, when v = 0 and only M ₁ ² obtained in the equation (26) is the moving area M ² , the following equation (40) and further the equation (41) are obtained. In the evaluation of the equation (41), π is It is erased by the denominator and is no longer needed.

Ie

Therefore, in the evaluation of the equation (35), z and ρ are obtained as measured values in units of $ (dollars), the infinite multiplication factor k _∞ , and the radial and axial leakage ratios of the core system configured in the critical experiment apparatus 200 The effective delayed neutron ratio β _eff can be obtained by obtaining the ratio a, the critical water level zc, and the extrapolation distance δ. That is, although evaluation by calculation is necessary, the effective delayed neutron ratio β _eff can be obtained by using a calculated value with less error and less error based on today's calculation technology. Further, it is a feature of this embodiment that no special device is required for the measurement itself.

  As described above, in the present embodiment, the effective delayed neutron ratio can be accurately calculated without using any additional special equipment, using the facilities and experimental techniques that the normal critical experiment apparatus 200 has. it can.

  Although the present embodiment has been described above, the embodiment is presented as an example, and is not intended to limit the scope of the invention. For example, in the embodiment, the case where the present invention is applied to a critical experiment apparatus is shown, but the present invention is not limited to this. For example, in the case of a critical apparatus, the present invention can be applied to a research reactor if a similar procedure can be performed.

  Furthermore, the embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention.

  The embodiments and the modifications thereof are included in the scope of the invention and the scope of the invention, and are also included in the invention described in the claims and the equivalents thereof.

  DESCRIPTION OF SYMBOLS 10 ... Effective delayed neutron ratio measuring apparatus, 100 ... Central processing unit (CPU), 101 ... Bus, 110 ... Calculation part, 111 ... Experimental system effective delayed neutron ratio provisional value calculation part, 112 ... Experimental system physical quantity calculation part , 113 ... Experimental system axial extrapolation distance calculation unit, 114 ... Representative fuel rod cell infinite multiplication factor calculation unit, 115 ... Calculated value / measured value relative error calculation unit, 116 ... Experimental system sensitivity coefficient vector calculation unit, 117 ... Representative Fuel rod cell sensitivity coefficient vector calculation unit, 118 ... Covariance error matrix calculation unit, 119 ... Representative fuel rod cell infinite multiplication factor correction value calculation unit, 120 ... Representative fuel rod cell moving area calculation unit, 121 ... Experimental system effective delay Neutron ratio calculation unit, 130 ... storage unit, 131 ... experimental system measurement value storage unit, 132 ... experimental system effective delayed neutron ratio provisional value storage unit, 133 ... experimental system physical quantity storage unit, 134 Experimental system axial extrapolation distance storage unit, 135 ... representative fuel rod cell calculation value storage unit, 136 ... calculated value / measured value relative error storage unit, 137 ... experimental system sensitivity coefficient vector storage unit, 138 ... representative fuel rod cell sensitivity Coefficient vector storage unit, 139 ... covariance error matrix storage unit, 140 ... control unit, 141 ... input control unit, 142 ... output control unit, 150 ... input device, 160 ... output device, 200 ... critical experiment device, 201 ... core Tank, 202 ... Fuel support plate, 203 ... Upper lattice plate, 204 ... Lower lattice plate, 205 ... Core, 210 ... Fuel rod, 220 ... Control rod, 230 ... Neutron detector, 240 ... Water level transmitter

Claims (9)

A criticality that achieves criticality by adjusting the insertion length of the control rods into the core while holding the core tank holding the core in which a plurality of fuel rods are arranged horizontally spaced apart from each other. In the effective delayed neutron ratio measurement method for calculating the effective delayed neutron ratio of the device,
A test step in which the input device acquires the measurement time of the multiplication time t and the axial fission rate distribution of the fuel rod when the control rod is fully pulled out from the critical state;
After the test step, a reactivity etc. calculating step for calculating the reactivity ρ and the axial extrapolation distance δ using the multiplication time t and the measurement result of the axial fission rate distribution;
After the reaction of such calculation step calculates the infinite multiplication factor k _∞, the axial fission rate distribution and the reactor core to correct the infinite multiplication factor k _∞ from the measured value of the critical water level zc at the time of a critical A correction step;
After the correcting step, a critical water level calculating step for calculating the critical water level zc at the time of full withdrawal of the control rod;
A final value calculating step for calculating a final value of the effective delayed neutron ratio β _eff after the critical water level calculating step;
Have
In the reactivity calculation step, the provisional value of the effective delayed neutron ratio β _eff is calculated, and the provisional value of the effective delayed neutron ratio β _eff is used. Measuring method. In the reactivity calculation step, the reactivity ρ is calculated using the provisional value of the multiplication time t and the effective delayed neutron ratio β _eff obtained in the test step, and the criticality is obtained when all control rods are drawn from the values. The water level reactivity coefficient is calculated by determining the water level difference of the current core tank water from the virtual critical water level and the water level, and the effective delayed neutron ratio β _eff of the core is calculated from these results. The effective delayed neutron ratio measuring method according to claim 1. The effective delayed neutron ratio measuring method according to claim 1 or 2, wherein, in the final value calculating step, an effective delayed neutron ratio β _{eff is obtained} by the following equation.

(Where k _eff ^E is the effective neutron multiplication factor of the core system, k _∞ is the infinite multiplication factor of a typical fuel rod cell of the core system, and a is the leakage in the radial and axial directions of the core system configured in the critical experimental device. The ratio of the ratio is shown.) In the final value calculating step, using the provisional value of the effective delayed neutron fraction beta _eff, by the following equation, the mobile calculates the area M ₁ ^2, wherein the calculation of the critical water level zc, the second transfer area M ₂ calculation of ^2, synthesized effective delayed neutron fraction measuring method according to any one of claims 1 to 3, characterized in that each of the calculation of the transfer area M ² has.

5. The effective delayed neutron ratio measuring method according to claim 4, wherein in the final value calculating step, the effective delayed neutron ratio β _{eff is obtained} by the following equation.

In the step of calculating the reactivity, etc., a step of calculating a dynamic characteristic parameter by modeling the critical experimental apparatus in two or three dimensions using the relative value of the delayed neutron ratio of the six groups, the relative value and the multiplication Substituting the time t into the inverse time equation to obtain the reactivity ρ generated by pulling out all the control rods, and using the value of the reactivity ρ for calculating the effective delayed neutron ratio β _eff The method for measuring the effective delayed neutron ratio according to any one of claims 1 to 5. In the reactivity calculation step, the reactivity ρ is multiplied by the provisional value of the effective delayed neutron ratio β _eff and the result is added to 1 to obtain an effective neutron multiplication factor k _eff ^E of the core. The effective delayed neutron ratio measuring method according to any one of claims 1 to 6, wherein the effective neutron multiplication factor k _eff ^E is used for calculating the effective delayed neutron ratio β _eff. . The step of calculating the reactivity, etc.
Obtaining an effective neutron multiplication factor k _eff ^E of the core using the reactivity ρ;
Calculating a critical state of the core with a three-dimensional Monte Carlo code to calculate a neutron effective multiplication factor k _eff ^C ;
Calculating a relative difference E _P = (k _eff ^C −k _eff ^E ) / k _eff ^E between the effective neutron multiplication factor k _eff ^C and the effective neutron multiplication factor k _eff ^E ;
Calculating a sensitivity coefficient vector S _R on Nuclear Data Library using the neutron infinite multiplication factor k _∞ of the core,
An experimental system sensitivity coefficient vector calculation unit calculating a sensitivity coefficient vector S _E related to the nuclear data library for the neutron effective multiplication factor k _eff ;
A step of said covariance error matrix of nuclear data library and is W, obtains the relative error ER _P of the neutron infinite multiplication factor k _∞ due to nuclear data library by the following equation,
^{_{ER P = E P × (S}} R T WS R) / (S E T W R)
(However, T represents a transposed matrix.)
Using the obtained relative error ER _P, determining a infinite multiplication factor k _∞ ^correction of the fuel rod cells of interest by the following equation,
k _∞ ^correction = k _∞ × 1 / (1 + ER _P )
Have
The effective delay according to any one of claims 1 to 7, wherein the infinite multiplication factor k _∞ ^correction of the fuel rod cell for the purpose is used for calculating the effective delayed neutron ratio β _eff. Neutron ratio measurement method. The length of insertion of control rods extending in the vertical direction into the core while holding a predetermined water level inside the tank containing the core in which a plurality of fuel rods extending in the vertical direction are horizontally spaced and arranged in a grid In the effective delayed neutron ratio measuring device that calculates the effective delayed neutron ratio of the critical device that adjusts the thickness to achieve the criticality,
An input device that accepts external input of data obtained from experiments;
An experimental system measurement value storage unit for storing data received by the input device;
An experimental system for calculating the provisional value of the effective delayed neutron ratio _βeff ;
An experimental system effective delayed neutron ratio provisional value storage unit for storing a temporary value of the effective delayed neutron ratio _βeff calculated by the experimental system effective delayed neutron ratio provisional value calculation unit;
The axial and lateral neutron flows are calculated, the ratio of lateral leakage to axial leakage is calculated, and the multiplication time t based on the signal from the neutron detector stored in the experimental system measurement value storage unit. , Calculation of reactivity ρ applied to the critical experiment apparatus using the provisional value of the effective delayed neutron ratio _βeff stored in the multiplication time t and the experimental system effective delayed neutron ratio provisional value storage unit The calculation of the water level zc that is just critical when all the control rods are extracted from the experimental condition data stored in the experimental system measured value storage unit, and the effective neutron multiplication factor in the fully extracted state of the control rod at the water level during the test an experimental system physical quantity calculation unit for calculating k _eff ;
Experimental system physical quantity that stores calculation results such as the ratio of the lateral leakage to the axial leakage calculated by the experimental system physical quantity computing unit, the reactivity ρ, the water level zc, and the neutron effective multiplication factor k _eff. A storage unit;
An experimental system axial extrapolation distance computing unit that calculates an axial output distribution f (x) including the extrapolation distance δ in the axial direction based on the axial output distribution data stored in the experimental system measurement value storage unit;
An experimental system axial extrapolation distance storage unit that stores an output distribution including the axial extrapolation distance calculated by the experimental system axial extrapolation distance calculation unit;
The experimental condition data stored in the experimental system measured value storage unit is used to calculate the infinite multiplication factor k _∞ of the fuel rod cell representing the core system, and the selected calculation method and calculation output from the input device A representative fuel rod cell infinite multiplication factor calculation unit for calculating the effective neutron multiplication factor k _eff ^C of the core system using the code;
A representative fuel rod cell calculation value storage unit for storing an infinite multiplication factor k _∞ of a fuel rod cell representing the core system calculated by the representative fuel rod cell infinite multiplication factor calculation unit;
The calculation result k _eff ^C of the neutron effective multiplication factor evaluated by the experiment system physical quantity calculation unit is compared with the experiment result k _eff ^E, and the absolute value of the difference | k _eff ^C −k _eff ^E | / k _eff ^E is calculated. further, the absolute value _| a _{/ k eff} ^E is calculated values and measurement values relative error calculation unit equal to or smaller than the prescribed value, _| ^k eff _C ^-k eff E
A calculated value / measured value relative error storage unit for storing the absolute value | k _eff ^C −k _eff ^E | / k _eff ^E calculated by the calculated value / measured value relative error calculation unit;
Suitable calculation technique, nuclear data library, the calculation code, with the experimental system sensitivity coefficient vector calculating portion for calculating a sensitivity coefficient vector S _E of the effective multiplication factor k _eff in experimental systems,
An experimental system sensitivity coefficient vector storage unit for storing a sensitivity coefficient vector S _E of the effective multiplication factor k _eff in the experimental system calculated by the experimental system sensitivity coefficient vector calculation unit;
A representative fuel rod cell sensitivity coefficient vector calculating portion for calculating a sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representing the core,
A representative fuel rod cell sensitivity coefficient vector storage unit for storing the sensitivity coefficient vector S _R of infinite multiplication factor k _∞ of the fuel rod cells representative of core calculated by said representative fuel rod cell sensitivity coefficient vector calculation part,
A covariance error matrix calculation unit for calculating the covariance error matrix W of the nuclear data library;
A covariance error matrix storage unit for storing the covariance error matrix W calculated by the covariance error matrix calculation unit;
Calculation of the relative error E _P included in the calculated value k _eff ^C evaluated by the experimental system physical quantity calculation unit, the sensitivity coefficient vector S _E stored in the experimental system sensitivity coefficient vector storage unit, and the representative fuel rod cell sensitivity coefficient and calculation of the correction factor CF by using said covariance error matrix W stored as the sensitivity coefficient vector S _R stored in the vector storage unit to the covariance error matrix storage unit, the relative error E _P and modifiers calculation of relative error ER _P due to the input parameter using the CF, the input parameter due to the correction of the relative error ER _P neutron infinite multiplication factor k _∞ using representative fuel rod cell infinite multiplication factor correction value calculation unit When,
A ratio of the lateral leakage to the axial leakage stored in the experimental system physical quantity storage unit, the reactivity ρ, the water level zc, the effective neutron multiplication factor k _{eff, and the} like, and the experimental system effective delayed neutron by using the provisional value of the stored effective delayed neutron fraction beta _eff in proportion provisional value storage unit, the calculation of the transfer area M ₁ ^2, the second calculation of the transfer area M ₂ ^2, and the transfer area M ₁ ² a representative fuel rod cell transfer area calculating unit for calculating the movement area M ² which were synthesized with the transfer area M ₂ ^2,
Using the movement area M ² calculated by the representative fuel rod cell movement area calculation unit, the corrected k _∞ calculated by the representative fuel rod cell infinite multiplication factor correction value calculation unit, the effective neutron multiplication factor k _{eff, and the} like. , An experimental system effective delayed neutron ratio calculator that calculates the final value of the effective delayed neutron ratio β _eff ,
An effective delayed neutron ratio measuring apparatus comprising:

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